Give your suggestions and how you caught mespirit here

Well there are a ton of ways to do it, but the easiest IMO in DPP is to get a Murkrow. They appear at a higher level, learn mean look and have immunity to Mespirit's psychic attack. However the best pokemon to do this will always be smeargle in my opinion, spore, mean look, false swipe, and recover. Anyways, get a pokemon that knows Mean Look/Block, got to an area that has 2 routes close together with tall grass. Go back and forth between the routes, stopping to check if mespirit is in your area on the map marker app you get from the poketch company. Once you see it there go to the grass and find it. Mean look it so it can not flee, and do what you would normally do from there. However if the pokemon you have is switched out or faints without baton passing the mean look mespirit can flee. If you use a quick ball, use it turn one-five with a 4x catch rate, after every 5 turns it goes down to 3x, 2x, etc. After that use dusk ball at night or ultra balls will work somewhat well during the day.

Hope this helps, oh and here is a reallllly annoying guys video on how he did it.

For Pearl, you can replace Murkrow with Misdreavus/Mismagius, which is what I used (since they also get Mean Look). They're immune to Swift and have alright HP so you can just take hits and heal every now and then. Plus, Shadow Ball can take off a significant chunk of its health without killing it if you're not that high-leveled. (That was my strategy, anyway. I don't know how well it'd work for somebody else.)

I heartily recommend hunting it at night, as Dusk Balls are lovely. Since the battle will probably take a while, I'd pack some Timer Balls too. Just watch out for Struggle.. it'd kinda suck if you dragged the battle on so long that it ran out of PP. :p